\subsection{}
From point of the view of sec. \ref{sec:20100823}, the pauli blocking is isolated.  But it is hard to tell the broad resonance from the narrow one except that the close-channel weight is smaller or larger.  In some sense, the narrow/broad resonance is an effect nor stemmed from pure pauli-blocking, but the real interaction. So the problem probably does not show up until we bring the interaction in.   

\subsection{}
One thing probably misses me a long time is that \emph{in BEC side, or close-channel molecule, $u_{k}$ is always close to 1, $F_{k}$ is always small.}  This potentially might simplify things.  